Geodesic
Stationary distribution of Jackson networks with an exponential constraint on the sojourn time of claims
Problemy fiziki, matematiki i tehniki, no. 3 (2020), pp. 73-77.

Voir la notice de l'article provenant de la source Math-Net.Ru

An exponential queuing network containing nodes of two types — single-line and multi-line is considered. In contrast to Jackson networks, the sojourn time at the nodes of the network is a random variable, the conditional distribution of which is exponential for a fixed number of claims in the node. For single-line nodes, the routing matrices of the served and non-served customers are, generally speaking, different, and for multi-line nodes they coincide. A sufficient ergodicity condition is established and a stationary distribution is found.
Keywords: open queuing network, single-line and multi-line nodes, limited sojourn time, ergodicity condition, stationary distribution. 
@article{PFMT_2020_3_a11,
     author = {Yu. V. Malinkovskii and V. A. Niamilastsivaya},
     title = {Stationary distribution of {Jackson} networks with an exponential constraint on the sojourn time of claims},
     journal = {Problemy fiziki, matematiki i tehniki},
     pages = {73--77},
     publisher = {mathdoc},
     number = {3},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PFMT_2020_3_a11/}
}
TY  - JOUR
AU  - Yu. V. Malinkovskii
AU  - V. A. Niamilastsivaya
TI  - Stationary distribution of Jackson networks with an exponential constraint on the sojourn time of claims
JO  - Problemy fiziki, matematiki i tehniki
PY  - 2020
SP  - 73
EP  - 77
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PFMT_2020_3_a11/
LA  - ru
ID  - PFMT_2020_3_a11
ER  - 
%0 Journal Article
%A Yu. V. Malinkovskii
%A V. A. Niamilastsivaya
%T Stationary distribution of Jackson networks with an exponential constraint on the sojourn time of claims
%J Problemy fiziki, matematiki i tehniki
%D 2020
%P 73-77
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PFMT_2020_3_a11/
%G ru
%F PFMT_2020_3_a11
Yu. V. Malinkovskii; V. A. Niamilastsivaya. Stationary distribution of Jackson networks with an exponential constraint on the sojourn time of claims. Problemy fiziki, matematiki i tehniki, no. 3 (2020), pp. 73-77. http://geodesic.mathdoc.fr/item/PFMT_2020_3_a11/

[1] B.V. Gnedenko, I.N. Kovalenko, Vvedenie v teoriyu massovogo obsluzhivaniya, Nauka, M., 1987, 431 pp.

[2] E.A. Kovalev, “Seti massovogo obsluzhivaniya s ogranichennym vremenem ozhidaniya v ocheredyakh”, AVT, 1985, no. 2, 50–55

[3] O.V. Yakubovich, “Statsionarnoe raspredelenie seti massovogo obsluzhivaniya s razlichnymi tipami signalov i polozhitelnykh zayavok i ogranicheniem na vremya prebyvaniya”, Izvestiya Gomelskogo gosudarstvennogo universiteta im. F. Skoriny, 2008, no. 5(50)-2, 207–211

[4] O.V. Yakubovich, V.E. Evdokimovich, “Set massovogo obsluzhivaniya so sluchainym vremenem prebyvaniya polozhitelnykh, otritsatelnykh zayavok i signalov”, Problemy fiziki, matematiki i tekhniki, 2010, no. 4(5), 63–67

[5] Yu.E. Letunovich, “Neodnorodnye seti s ogranicheniem na vremya prebyvaniya v rezhimakh obsluzhivaniya”, AVT, 2010, no. 5, 33–41 | MR

[6] O.V. Yakubovich, Yu.E. Dudovskaya, “Mnogorezhimnaya set massovogo obsluzhivaniya so sluchainym vremenem prebyvaniya razlichnykh tipov otritsatelnykh zayavok”, Problemy fiziki, matematiki i tekhniki, 2012, no. 4 (137), 74–77

[7] Yu.V. Malinkovskii, “Seti Dzheksona s odnolineinymi uzlami i ogranichennym vremenem prebyvaniya ili ozhidaniya”, AVT, 2015, no. 4, 67–78

[8] Yu.V. Malinkovskii, “Statsionarnoe raspredelenie veroyatnostei sostoyanii G-setei s ogranichennym vremenem prebyvaniya”, AVT, 2017, no. 10, 155–167